1. Stochastic Modeling & Simulation Lecture 6: Intro to Project Management – CPM

2. Administrative Problem Set 2 Any issues? Problem Set 1 grading Hopefully finishing soon. Problem Set 3… hopefully tomorrow afternoon.

3. Conditional Expectation Example Sumif and countif

4. Project Management Project management is a large area and can be the subject of entire courses. This is a mini introduction to some basic project management skills / tools We’ll (eventually) be using simulation to capture a more realistic picture of project planning and evaluation. Many facets to managing projects “Softer” skills: effective leadership, communications strategies, foster cooperation, etc. Management Science / quantitative skills  what we’ll be focusing in on for the next couple of lectures. Don’t have time to do advanced topics but a little bit can go a long way.

5. Project Management Tools Dimensions of Project Management 1. Time How long will a project take to complete? Which tasks will form bottlenecks? Which tasks can be delayed without causing increased project duration? 2. Resources How much money will it cost? How many people are needed? Are they needed for the entire duration of the project? 3. Scope What’s the purpose of the project? What are the deliverables? How are you measuring the success of the project? Two techniques we’ll discuss to address (1) and (2): Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT). While coming from different histories, these are essentially the same method, but we’ll discuss CPM as the deterministic version of PERT.

6. Critical Path Method A few things must be known (or assumed) for the CPM 1. The tasks that comprise the project Making an omelet: break the eggs, mix them up, fry in a skillet, etc. 2. The precedence relationships among the tasks You must break the eggs before you mix them 3. The time required to complete each task. It takes 5 minutes for the mixture to fry. Sounds easier than it some times is in practice. When you’re trying to figure out (1), (2) and (3) a white board is often helpful.

7. Network description Activity on Node (AON) network description: Once you have the list of tasks: A, B, …, E Draw them on a white board such that each node of a the network represents the tasks and how long you think each will take. The arcs between the nodes denote the order of events. Include Start and Finish nodes with zero duration NodePredecessorSuccessorDuration ANoneD, E8 BNoneC10 CBE3 DANone12 EA, CNone6

8. Critical Path – forward pass To define the Critical Path of a project, there are a few things we need to define first: For tasks i and j with i being a predecessor of j: Let the duration of task j be denoted as d j Earliest start time of task j be denoted as ES j Earliest finish time of j be denoted as EF j

9. Critical Path – backward pass Similarly define for tasks i and j with i being a predecessor of j: Latest start time of task j be denoted as LS j Latest finish time of j be denoted as LF j And very importantly, the slack of a task is the difference between the latest start and the earliest start of a task: LS j – ES j. Slack is the amount of time a task can be extended without changing the duration of the overall project.

10. Critical Path The Project Completion Time is the ES Finish A critical task, or a bottleneck, is a task that has zero slack. Increasing the duration of the task will necessarily delay the project completion. The critical path is the set of all critical tasks. Viewed as a network, the critical path is the longest path through the network.

11. Open Project Scheduling.xls A company needs to construct a new LAN Through consultation with the systems expert, the project has 15 subtasks, each requiring different amounts of time CPM – an example

13. CPM - Example Project completion time? 62 days = ES Finish How many nodes have slack? 7 Good to know and track progress. Delays happen. How will a delay or increase in a duration of a task effect the project duration is important to know.

14. Gantt Chart

15. Monitoring Resources Next time Projects require resources (time and money). What are the needs of the project over the duration duration of the project? What are our cash/expenditure needs per period (week, month, year)? What if different tasks required different inputs? Who needs to be hired when? Can we spend more and speed up a project? Crashing. Whether to do this is often an optimization problem (which isn’t really what we’re supposed to do in this course). So we might not cover it as much as we could.

16. Next time: Uncertainty What happens when task durations are unknown? You might not want to plug in averages… Simulate! Allows us to answer questions of the form: How likely is it that the project finishes on time? Under budget? If it’s late, what is the probability it finishes in less than X amount of time? Even harder problems like what if Jane Bob and Alice are working on a project and Bob is notoriously late, what tasks should you assign to Bob? (can be a very difficult problem). I.e., correlated duration times. If we do crashing… how much will an addition investment of $Z dollars increase our chance of meeting the deadline? Sometimes we can crash but the risk involved might or might not make it worth it!